2008/03/25 by Roman Bezrukavnikov, Pavel Etingof, Bezrukavnikov, Roman +1
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.0803.3639
28 pages, latex; two new sections and an appendix containing arXiv:0706.4308 are added; Conjecture 4.4 (which was false) is replaced by a counterexample
arxiv created 2009/10/28 · arxiv updated 2009/12/01
We introduce parabolic induction and restriction functors for rational Cherednik algebras, and study their basic properties. Then we discuss applications of these functors to representation theory of rational Cherednik algebras. In particular, we prove the Gordon-Stafford theorem about Morita equivalence of the rational Cherednik algebra for type A and its spherical subalgebra, without the assumption that c is not a half-integer, which was required up to now. Also, we classify representations from category O over the rational Cherednik algebras of type A which do not contain an Sn-invariant vector, and confirm a conjecture of Okounkov and the first author on the number of such representations. In the second version we have added a result on the simplicity of the spherical Cherednik algebra of type A for -1<c<0, and a strengthened version of the main result of arXiv:math/0312474, as well as an appendix by the second author containing arXiv:0706.4308, on the reducibility of the polynomial representation of the trigonometric Cherednik algebra.